1. Field of the Invention
The present invention relates to a threshold matrix and gray level reproducing method and apparatus using the threshold matrix, and more specifically to a threshold matrix and gray level reproducing method and apparatus using the threshold matrix for converting input image data into binary or multivalue data in a gray level reproducing process.
2. Related Background Art
One of most used methods among conventionally known gray level reproducing methods is an error diffusion method.
In the error diffusion method, an input image is converted into a binary image or a multivalue image by comparing each pixel of this input image with a threshold, and at this time, an error (a quantizing error) between input and output values is weighted and diffused to predetermined adjacent pixels to preserve an image density. The image which was output by this method has excellent image quality and resolution, however, processing speed is low because the process itself is complicated. Further, in a dot pattern which is created by the error diffusion method, generally, a position to be dotted is different according to an input image, whereby it is difficult to predict a degree of mixture of colors. Thus, there is a drawback that color reproducibility is poor as compared with a later-described systematic dithering method.
Incidentally, an independent determination-type dithering method is known as the gray level reproducing method by which the process is simplified and thus processing speed is high. In the independent determination-type dithering method, a pixel value of an input image is compared with a threshold in one-to-one to determine an output value. In this method, since only a noticed (or remarked) pixel is independently processed, and its peripheral pixels are not processed, whereby processing speed is high.
The independent determination-type dithering method is further classified into two methods, i.e., a random dithering method and a systematic dithering method, in accordance with a difference of how to represent the threshold.
The random dithering method is the method by which the threshold is changed for each pixel at random. The dot pattern which was obtained by this method has a white noise characteristic, whereby there is an advantage that any moire does not occur. However, in this dot pattern, image quality is low because a graininess is insistent or outstand, whereby the random dithering method is hardly being used now.
On the other hand, the systematic dithering method is the method which uses a threshold matrix (also called a dither matrix, a mask or the like) that thresholds are arranged. The systematic dithering method is broadly classified into clustered-dot dithering and dispersed-dot dithering according to how to arrange the thresholds in the threshold matrix.
In the clustered-dot dithering, the dots thickly increase at the position corresponding to the center of the threshold matrix, as the number of gray levels increases. Since the dot pattern created in this method has a low spatial frequency, its image quality is low in a case where an output device of which the definition is relatively low is used. Thus, the clustered-dot dithering is used in a field of, e.g., printing of which the definition is high.
On the other hand, in the dispersed-dot dithering, the threshold matrix is designed such that a dot arrangement of an output pattern is spatially dispersed. As a representative of the dispersed-dot dithering, a Bayer-type systematic dithering method (“An Optimum Method For Two-Level Rendition Of Continuous-Tone Pictures” Bayer, Proc. IEEE Int. Conf. Commun., Conference Record, p.26–11, 1973) is known so far. In the Bayer-type systematic dithering method, since a threshold arrangement is extremely regular, when an input image having a uniform gray level is subjected to a halftone process, an output pattern which is extremely regular for the input images of all gray levels is created, whereby uniformity of the dot pattern is satisfactory. However, when an output device of which the definition is relatively low is used, there is a problem that a rough texture (dither pattern) is perceived at a period of the size (16×16 in case of 256 gray levels) of a threshold matrix. Further, when a periodic pattern is included in the input image, there is a problem that moire may occur in the output image. For this reason, in the output device of which the definition is relatively low, i.e., several hundreds of dots per inch (dpi), image quality is deteriorated as compared with the error diffusion method, whereby the Bayer-type systematic dithering method is not used for the purpose to obtain a high-quality halftone image.
On the other hand, in recent years, it came to be known to obtain excellent image quality in a case where a dot pattern of an output image is a blue noise pattern (“Dithering With Blue Noise” R. L. Ulichney, Proc. IEEE, vol. 76, No. 1, p. 56). The blue noise pattern is characterized with a power spectrum (a blue noise characteristic) which consists of noise components aperiodic, isotropic and having less low frequency components. Ulichney contrived a perturbed error diffusion method by introducing irregularity to the conventional error diffusion method, and thus achieved the blue noise pattern.
The method which was proposed to achieve this blue noise pattern by using the systematic dithering method is a blue noise masking method (Japanese Patent No. 2622429, U.S. Pat. No. 5,111,310, “Digital Half-toning Technique Using Blue-Noise Mask”, T. Mitsa and K. J. Parker, J. OptSoc. Am, vol. 9, No. 11, pp. 1920–1929 (1992)). When the input image having the gray level of uniform mask size is processed by using the blue noise masking method, the output dot pattern has the blue noise characteristic. Therefore, like the perturbed error diffusion method of Ulichney, any moire does not occur, and thus graininess is reduced as compared with the random dithering method. Further, as compared with the perturbed error diffusion method, the operation is simple, and thus processing speed is high.
However, in the dot pattern which is created by using the blue noise masking method, uniformity of the dot distribution is deteriorated according to the number of gray levels, whereby unevenness appears in the output image. Specifically, the noise is felt in the dot patterns adjacent to the minimum gray level and the maximum gray level.
The reason of such a problem is as follows. Namely, in the blue noise masking method, the dot pattern of intermediate gray level is optimized and created, and then the dot patterns of high and low gray levels are sequentially created, whereby degree of freedom for dot selection is low nearby the minimum and maximum gray levels, and thus it is difficult to obtain the ideal dot pattern. Specifically, when the blue noise masking method is used in an ink-jet printer, nonuniformity of the dot pattern in the low gray level part where the dots are sparsely arranged and such sparsity is visible has the room for improvement.
Further, a dot pattern creation method which repetitively uses two-dimensional discrete Fourier transform and two-dimensional inverse discrete Fourier transform is complicated, whereby there is a problem that it takes time to create the dot pattern.
As the systematic dithering method by which uniformity of the dot pattern is increased, there is the method disclosed in Japanese Patent Application Laid-Open No. 2000-59626. In this method, the uniformity of the dot pattern is maintained by using regularity of the dot pattern created by the Bayer-type systematic dithering method, and at the same time irregularity is introduced to the dot pattern to reduce the problems of dither pattern and moire.
Since the threshold matrix in this method includes plural same threshold structures, this matrix creates anisotropic and periodic dot patterns in all of the gray levels and has a characteristic opposite to the blue noise characteristic. Further, by eliminating redundancy of the information of the parts having the same threshold structure, a memory capacity to store the threshold matrices can be reduced.
On the other hand, in recent years, according as the ink-jet printer is widespread, demands of general users for image quality is highly developed. However, in the above method, though not so insistent, a texture (dither pattern) occasionally appears slightly in the longitudinal, lateral or diagonal direction along which the plural same structures are arranged, in accordance with the gray level, and thus this method has the room for improvement.